诱导I-Fuzzy拓扑空间

本文引入了生成I-Fuzzy拓扑空间的概念,研究了Fuzzifying拓扑空间(X,τ)与其相应的生成I-Fuzzy拓扑空间(IX,ω(τ))的联系;然后介绍了ω,ι算子及它们的运算性质;最后给出并研究了I-Fuzzy诱导空间,I-Fuzzy弱诱导空间,I-Fuzzy满层空间的定义和它们间的联系.     

Locally Closed Semirings and Iteration Semirings

Locally closed semirings, iteration semirings and Conway semirings play an important role in the algebraic theory of semirings and theoretical computer science. Z. ésik and W. Kuich showed that a locally closed commutative semiring is an iteration semiring (is also a Conway semiring). By study of polynomial semirings and matrix semirings, we obtain new expressions of certain polynomials and show that all matrix semirings over a locally closed semiring are also locally closed, and so a locally closed semiring (which need not be commutative) is an iteration semiring.     

Dualities of groups

Summary The existence of Tarski groups and other infinite groups with restricted subgroup lattices show that there are non-soluble groups with a duality. The present work finds restrictions imposed on an arbitrary group by the existence of a duality and studies some particular kinds of dualities.The authors are grateful to the British Council and C.N.R. for financial support during the preparation of this paper.     

Locally Closed Semirings and Iteration Semirings

Locally closed semirings, iteration semirings and Conway semirings play an important role in the algebraic theory of semirings and theoretical computer science. Z. ésik and W. Kuich showed that a locally closed commutative semiring is an iteration semiring (is also a Conway semiring). By study of polynomial semirings and matrix semirings, we obtain new expressions of certain polynomials and show that all matrix semirings over a locally closed semiring are also locally closed, and so a locally closed semiring (which need not be commutative) is an iteration semiring.     

诱导超空间连续流的拓扑传递性

(X,f)为紧拓扑空间X上的连续流,(K(X),f)是由(X,f)诱导的紧超空间K(X)上的连续流.研究了(X,f)和(K(X),f)拓扑传递性之间的关系.证明了如果(X,f)是拓扑传递的,那么(K(X),f)也一定是拓扑传递的,并且举例证明了其逆命题不成立.进一步证明了(K(X),f)拓扑传递的当且仅当(X,f)是弱混合的.     

Natural Dualities

Let S be an arbitrary associative ring and _S W be a left S-module. Denote by R the ring End _S W and by both the contravariant functors Hom _S (–,W) and Hom _R (–,W). A module M is reflexive if the evaluation map _M : M² M is an isomorphism. Any direct summand of finite direct sums of copies of _S W and of R _R is reflexive. Increasing in a minimal way the classes of reflexive modules, a cotilting condition on finitely generated R-modules naturally arises.     

G-Prime Ideals in Semirings and Their Skew Group Semirings

Semirings have been studied by various researchers either in an attempt to broaden the techniques coming from semigroup theory or generalization of group theory and ring theory. From an algebraic point of view, semirings provide the most natural generalization of the theory of rings. In this article, we generalize some of the results of Lorenz and Passman (1979 Lorenz , M. , Passman , D. S. ( 1979 ). Prime ideals in crossed products of finite groups . Israel J. Math. 33 ( 2 ): 89 – 132 .[Crossref], [Web of Science ®] , [Google Scholar]) for semirings with finite group action on them.     

拟阵闭包算子诱导拓扑空间的分离性

拟阵是图论与代数的结合,而拓扑学是一门重要的数学基础学科.利用拟阵理论研究拓扑空间,从而将两者进行融合,通过拟阵的闭包算子定义拟阵拓扑空间,进一步利用拟阵闭包算子与拓扑闭包算子之间的关系,讨论拟阵拓扑空间的分离性.     

Dualities in full homomorphisms

In this paper we study dualities of graphs and, more generally, relational structures with respect to full homomorphisms, that is, mappings that are both edge- and non-edge-preserving. The research was motivated, a.o., by results from logic (concerning first order definability) and Constraint Satisfaction Problems. We prove that for any finite set of objects (finite relational structures) there is a finite duality with to the left. It appears that the surprising richness of these dualities leads to interesting problems of Ramsey type; this is what we explicitly analyze in the simplest case of graphs.     

Congruence-Simple Semirings

Several classes of congruence-simple semirings are characterized and various further examples are constructed. Among others, it is shown that every congruence-simple semiring fits into one of the following three classes: additively idempotent semirings, additively cancellative semirings, additively nil-semirings of index 2.     

Choice-Free Dualities for Domains

A basic tool in domain theory and point-free topology are (Scott) open filters in a partially ordered set. A systematic investigation of that concept shows that central notions and facts like Lawson’s famous self-duality of the category of continuous domains may be established without invoking any choice principles, if only continuous domains are replaced by so-called δ-domains, which coincide with the former in the presence of dependent choices. Many of the conclusions remain valid for the more flexible notion of ζ-domains, comprising important variants such as algebraic or hypercontinuous domains.     

Natural and Doubly Natural Dualities

Representable dualities between categories of modules satisfying natural closure properties are investigated and shown to be determined by homological properties shared by various classical and recently investigated types of dualities.     

半环上的粗糙集

利用同余关系把粗糙集理论引入到半环里,给出了半环中的一个子集的上,下近似的概念,并研究了其一系列性质;另外我们还讨论了半环中的粗糙理想及性质.